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Source and Listener Moving in Different Lines

If a vibratin...

Question

If a vibrating tuning fork of frequency 255Hz is approaching with a velocity 4m/s perpendicular to a wall. The number of beats produced per sec is: (speed of sound in air = 340m/s)

A

3

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B

4

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C

5

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D

6

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Solution

The correct option is B 3
$V_{s} = 4 m s^{- 1}$
Apparent frequency, $f^{'} = (\frac{V}{V - V_{s}}) f$ $= (\frac{340}{340 - 4}) 255$
The wall appears as source with observer moving to stationary source.
$f_{2} = (\frac{V + V_{0}}{V}) f$
$= (\frac{340 + 4}{340}) 255$
Beats $= f_{2} - f^{'} = (\frac{344}{340} - \frac{340}{336}) 255$ $= 3 H z$

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